Duality Protected Multi-Criticality in Deconfined Quantum Phase Transitions

Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the duality can be promoted as a symmetry, this leads to the multicriticalities. For example, the deconfined quantum critical point has self-dual descriptions. This work investigates the multicritical behavior of this kind of theory under perturbative deformation. To be specific, the QED3 with the Chern-Simons term is used to describe such quantum phase transitions, and the Gross-Neveu term is introduced to describe the multicriticality. By doing the large-N renormalization group analysis, we find the multicriticality falls in different universality classes from the corresponding nearby continuous transitions. Scaling dimensions of the possible non-relativistic 4-fermion interactions are calculated, these operators have their counterparts in the lattice models. Specifically, our calculation shows certain spin-spin interactions will drive the deconfined quantum criticality to first order as found in previous numerical studies.